Efficient features for shape analysis of lesions in breast MR

ABSTRACT

A method for analyzing a shape of a region of interest in a medical image of a body part, including: finding a region of interest in the medical image; calculating a Reeb graph of the region of interest, and determining whether the region of interest is a malignant lesion candidate based on a shape characteristic of the Reeb graph.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application No.60/971,668, filed Sep. 12, 2007, the disclosure of which is incorporatedby reference herein in its entirety.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates to detecting lesions in medical images,and more particularly, to using efficient features for shape analysis oflesions in breast MR.

2. Discussion of the Related Art

A key process of detecting regions in breast MR, also referred to asmagnetic resonance breast imaging, involves shape analysis andpharmacokinetic analysis of candidate regions. Most of the existingshape features are scalars that reflect, to some extent, the complexityof the lesion boundary. A popular shape feature is the square root ofthe surface area S^(1/2) divided by the cubic root of the volume V^(1/3)of a candidate region. See [Chen, W. and Giger, M. L. and Bick, U. AFuzzy C-Means (FCM)-Based Approach for Computerized Segmentation ofBreast Lesions in Dynamic Contrast-Enhanced MR Images. Acad. Radiol.,13(1):63-72, 2006], for example. This feature shows how the shapedeviates from a sphere, because a sphere attains the minimum ofS^(1/2)/V^(1/3).

Another well-known shape feature is fractal dimension, which is a scalarthat is used, for example, in ONCAD by Penn Diagnostics and is describedin Penn at al. [Penn, A. I., Loew, M. H. Estimating Fractal Dimensionwith Fractal Interpolation Function Models. IEEE Trans. Med. Imaging,16(6):930-937, 1997], for example. The fractal dimension of an ordinaryshape coincides with the ordinary definition of integer dimensions suchas three dimensions for medical volumes. For a fractal shape that isdefined recursively or by infinite iterations, its fractal dimension ishigher than ordinary shapes and is a fractional number such as 3.55.Penn et al. used the fractional number to represent the complexity ofthe carcinoma shape. However, a carcinoma cannot have a dimension otherthan integers in a strict mathematical sense because it is not definedrecursively nor by infinite iterations. Such scalars have limiteddescriptive power because they are only a one-dimensional projection ofa very complicated feature.

SUMMARY OF THE INVENTION

In an exemplary embodiment of the present invention, a method foranalyzing a shape of a region of interest in a medical image of a bodypart, comprises: finding a region of interest in the medical image;calculating a Reeb graph of the region of interest; and determiningwhether the region of interest is a malignant lesion candidate based ona shape characteristic of the Reeb graph.

The shape characteristic comprises a number of branches in the Reebgraph, and when the number of branches is above a threshold the regionof interest is a malignant lesion candidate.

The shape characteristic comprises a number of branches in the Reebgraph that are above a length, and when the number of branches is abovea threshold the region of interest is a malignant lesion candidate.

The method further comprises choosing a function from which to calculatethe Reeb graph. The function is an isolation measure that is computedfor each voxel in the region of interest.

The shape characteristic comprises a value that is obtained by dividinga value obtained from the isolation measures by a power of a volume ofthe region of interest, and when the value of the shape characteristicis above a threshold the region of interest is a malignant lesioncandidate.

The value obtained from the isolation measures is an average of theisolation measures, a median of the isolation measures, a maximum of theisolation measures or a combination of the average, median or maximum ofthe isolation measures.

The power of the volume of the region of interest is a square root or acubic root of the volume of the region of interest.

The isolation measure is represented by:μ(v)=∫_(pεS) g(v,p)dS,where v is a point of S at which to calculate μ, p is a point of S,g(v,p) is a function that returns a distance between v and p of S, S isa portion of the region of interest and μ(v) is a mean of a distancefrom v to all points of S. S is a surface of the region of interest. Thedistance is a geodesic distance or a Euclidean distance.

The function is a radial unction that is computed for each voxel in theregion of interest.

The radial function is represented by:μ(v)=d(v,c),where d(v,c) is a Euclidean distance between v and c, c is a point ofthe region of interest and v is a point of the region of interest atwhich to calculate μ. c is a centroid or a center of the region ofinterest.

The medical image comprises a magnetic resonance image or a computedtomography image.

The body part comprises a breast, a lung or liver.

In an exemplary embodiment of the present invention, a system foranalyzing a shape of a region of interest in a medical image of a bodypart, comprises: a memory device for storing a program; a processor incommunication with the memory device, the processor operative with theprogram to: find a region of interest in the medical image; calculate aReeb graph of the region of interest; and determine whether the regionof interest is a malignant lesion candidate based on a shapecharacteristic of the Reeb graph.

In an exemplary embodiment of the present invention, a method foranalyzing a shape of a region of interest in a medical image of a bodypart, comprises: finding a region of interest in the medical image;calculating an isolation measure for each voxel in the region ofinterest; and determining whether the region of interest is a malignantlesion candidate by using the isolation measures.

In an exemplary embodiment of the present invention, a system foranalyzing a shape of a region of interest in a medical image of a bodypart, comprises: a memory device for storing a program; a processor incommunication with the memory device, the processor operative with theprogram to: find a region of interest in the medical image; calculate anisolation measure for each voxel in the region of interest; anddetermine whether the region of interest is a malignant lesion candidateby using the isolation measures.

The foregoing features are of representative embodiments and arepresented to assist in understanding the invention. It should beunderstood that they are not intended to be considered limitations onthe invention as defined by the claims, or limitations on equivalents tothe claims. Therefore, this summary of features should not be considereddispositive in determining equivalents. Additional features of theinvention will become apparent in the following description, from thedrawings and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a Torus in (a) and its Reeb graph in (b) using a heightfunction;

FIG. 2 shows examples of the distribution of the function μ and itsisovalued contours for Topology Matching: (a) sphere; (b) cube, (c)tours and (d) cylinder;

FIG. 3 is an example of a deformed shape in (a) and (b) showingdistribution of the function μ;

FIG. 4 is a flow diagram of a method for detecting lesions in medicalimages via shape analysis in accordance with an exemplary embodiment ofthe present invention;

FIG. 5 is a flow diagram of a method for detecting lesions in medicalimages via shape analysis in accordance with an exemplary embodiment ofthe present invention; and

FIG. 6 is a block diagram of a system in which exemplary embodiments ofthe present invention may be implemented.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

As discussed in the Background section of this disclosure, most of theshape features used in breast MR are scalars that have limiteddescriptive power. In accordance with an exemplary embodiment of thepresent invention, we use a graph structure to represent shapes oflesions in breast MR. The use of the graph structure can representdetailed shapes that help in discriminating lesions. For example, themethod and system disclosed herein can be used to shortlist thecandidates of malignant lesions so that radiologists can quicklyscrutinize a small number of regions of interest.

In accordance with an exemplary embodiment of the present invention, weuse a graph called the Reeb graph to represent a lesion shape. Reebgraphs were introduced to the computer graphics and vision community byone of the inventors of this application in [Y. Shinagawa and T. L.Kunii. Constructing a Reeb Graph Automatically from Cross Sections. IEEEComp. Graph. and Applications, 11(6):44-51, 1991], the disclosure ofwhich is incorporated by reference herein in its entirety. The graphrepresents a skeleton-like structure that characterizes the shape of thelesion. To calculate the Reeb graph, we define a function ƒ on theobject M (regarded as a manifold). For this purpose, we have chosen theaverage geodesic distance function which came to be known as theisolation measure that is rotationally invariant, proposed in [M.Hilaga, Y. Shinagawa, T. Kohmura and T. L. Kunii. Topology Matching forFully Automatic Similarity Estimation of 3D Shapes. SIGGRAPH 2001, pp.203-212], the disclosure of which is incorporated by reference herein inits entirety. The Reeb graph is then defined as the quotient space ofƒ(M) with respect to an equivalence relation—where points p and q areequivalent if ƒ(p)=ƒ(q) and ƒ⁻¹(p) and ƒ⁻¹(q) belong to the sameconnected component.

The calculation of the isolation measure in [M. Hilaga, Y. Shinagawa, T.Kohmura and T. L. Kunii. Topology Matching for Fully AutomaticSimilarity Estimation of 3D Shapes. SIGGRAPH 2001. pp. 203-212] wasproportional to n² log n using Dijkstra's algorithm for obtaining theshortest paths where n is the number of object voxels. For rapidcalculation of the isolation measure ƒ, we propose a sampling strategy;i.e., we subdivide the object voxels into N groups and calculate theisolation measure of each group one by one. If the mean of the isolationmeasure is within a tolerance, we use the average of the group isolationmeasures as the inferred value. Otherwise, we continue the groupwisecalculation until the values become statistically robust.

In our experiments, we calculated candidate regions of interest fromDynamic Contrast Enhanced Magnetic Resonance (MR) Images of breasts bydetecting rapid enhancements. After computing the isolation measure of acandidate region of interest, we constructed its Reeb graph. We foundthat the average isolation measure divided by V^(1/2) and the number ofbranches in the Reeb graph are useful features to discriminate malignantlesions.

A more detailed discussion of the Reeb graph and the Isolation Measurewill now be presented.

Reeb Graph

A Reeb graph is a topological and skeletal structure for an object ofarbitrary dimensions. In Topology Matching, the Reeb graph is used as asearch key that represents the features of a 3D shape. The definition ofa Reeb graph is as follows:

Definition: Reeb graph—Let μ:C→R be a continuous function defined on anobject C. The Reeb graph is the quotient space of the graph of μ in C×Rby the equivalent relation (X₁,μ(X₁))˜(X₂,μ(X₂)) which holds if an onlyif

-   -   μ(X₁)=μ(X₂), and    -   X₁ and X₂ are in the same connected component of μ⁻¹(μ(X₁)).

When the function μ is defined on a manifold and critical points are notdegenerate, the function μ is referred to as a Morse function, asdefined by Morse theory in [Y. Shinagawa, T. L. Kunii and Y. L.Kergosien. Surface Coding Based on Morse Theory. IEEE Computer Graphicsand Applications, Vol. 11. No. 5, pp. 66-78, September 1991], forexample; however, Topology Matching is not subject to this restriction.

If the function μ changes, the corresponding Reeb graph also changes.Among the various types of μ and related Reeb graphs, one of thesimplest examples is a height function on a 2D manifold. That is, thefunction μ returns the value of the z-coordinate (height) of the point von a 2D manifold:μ(v(x,y,z))=z.

Many studies have used the height function as the function μ forgenerating the Reeb graph, see [Y. Shinagawa, T. L. Kunii and Y. L.Kergosien. Surface Coding Based on Morse Theory. IEEE Computer Graphicsand Applications, Vol. 11, No. 5, pp. 66-78, September 1991, M. de Bergand M. van Kreveld. Trekking in the Alps Without Freezing or GettingTired. Algorithmica, Vol. 18, pp. 306-323, 1997, M. van Kreveld, R. vanOstrum, C. Bajaj, V. Pascucci and D. Schikore. Contour Trees and SmallSeed Sets for Isosurface Traversal. Proc. Symp. Computational Geometry,pp. 212-220, 1997, S. Takahashi, Y. Shinagawa and T. L. Kunii. AFeature-based Approach for Smooth Surfaces. Proc. Symp. Solid Modeling,pp. 97-110, 1997 and S. P. Tarasov and M. N. Vyalyi. Construction ofContour Trees in 3D in O(n log n) Steps. Proc. Symp. ComputationalGeometry, pp. 68-75, 1998], for example.

FIG. 1 shows the distribution of the height on the surface of a torus in(a) and the corresponding Reeb graph in (b). On the left side of FIG. 1,red and blue coloring (represented by the shaded lower portion of theTorus and the shaded upper portion of the Torus, respectively)represents minimum and maximum values, respectively, and the black linesrepresent the isovalued contours. The Reeb graph on the right side ofFIG. 1 corresponds to connectivity information for the isovaluedcontours.

Isolation Measure

A Reeb graph is generated by a continuous function μ. If a differentfunction is used as μ, the Reeb graph will change. The function μ isdefined for the application in question. For example, in terrainmodeling applications or when modeling a 3D shape based on crosssections such as CT images, the height function has been a usefulfunction μ because these applications are strictly bound by height.However, the height function is generally not appropriate as a searchkey for identifying a 3D shape because it is not invariant totransformations such as object rotation. Though the use of curvature asthe function μ may provide invariance in a rotation, it is generally notappropriate as a search key for identifying a 3D shape, because a stablecalculation of curvature is difficult on a noisy surface, and smallundulations may result in a large change of curvature, causingsensitivity in the structure of the Reeb graph.

To define a function μ that is appropriate as a search key foridentifying a 3D shape, we use a geodesic distance, that is, thedistance from point to point on a surface. Using geodesic distanceprovides rotation invariance and resistance against problems caused bynoise or small undulations. In one case, Lazarus et al. [F. Lazarus andA. Verroust. Level Set Diagrams of Polyhedral Objects. Proc. Symp. SolidModeling, pp. 130-140, 1999] proposed a level set diagram (LSD)structure in which geodesic distance from a source point is used as thefunction μ. However, in this case, the function μ is only suitable forconstructing a reasonable set of cross sections of a 3D shape. To make asearch key for 3D shapes, the source point is determined automaticallyand in a stable way. However, a small change in the shape may result inan entirely different source point, creating an obstacle for theconstruction of a stable Reeb graph.

To avoid this, we construct the function μ at a point v on a surface Sas follows:μ(v)=∫_(pεS) g(v,p)dS   (1)where the function g(v,p) returns the geodesic distance between v and pon S. This function μ(v) has no source point and hence is stable, and itrepresents the degree of center or edge on a surface. Since μ(v) isdefined as a sum of a geodesic distance from v to all points on S, asmall value means that a distance from v to arbitrary points on thesurface is relatively small, that is, the point v is nearer the centerof the object.

Here, note that the function μ(v) is not invariant to scaling of theobject. To handle this issue, a normalized version of μ(v) is used:

${\mu_{n}(v)} = \frac{{\mu(v)} - {\min_{p \in S}{\mu(p)}}}{\max_{p \in S}{\mu(p)}}$

In this normalization, range(S)=max_(pεS)μ(p)-min_(pεS)μ(p) may also bea candidate for the denominator, however it is not employed because itamplifies errors when range(S) is small, particularly in the case of asphere, where range(S)=0. The value min_(pεS)μ(p) corresponds to a mostcentral part of the object, and a shift can be introduced to initiallymatch the centers of different objects when estimating similaritybetween them, as described below.

Examples of the function μ_(n)(v) defined on several primitive objectsare shown in FIG. 2 where the coloring has the same meaning as inFIG. 1. For example, although not shown, the sphere in image (a) iscompletely red, the cube in image (b) is completely red, but for theblack lines, the torus in image (c) is red in inner portion thereof andthe cylinder in image (d) is red in the center thereof. Notice that thesphere has a constant value of μ_(n)(v)=0 and more asymmetric shapeshave a wider range of values for μ_(n)(v).

The function μ_(n)(v) is particularly useful because it is resistant tothe type of deformation shown in FIG. 3. This is because the deformationdoes not drastically change the geodesic distance on the surface. Notethat the coloring in FIG. 3 has the same meaning as in FIG. 1. In FIG.3, the central shaded portion of the frog in (a) and (b) is red and thelower feet of the frog are blue.

Thus, the normalized integral of geodesic distance is suitable as thecontinuous function for Topology Matching.

A method for detecting lesions in medical images via shape analysis inaccordance with an exemplary embodiment of the present invention willnow be described with reference to FIG. 4.

As shown in FIG. 4, a region of interest is found in a medical image ofa body part (410). The region of interest can be found by using anysuitable image segmentation technique, such as snakes for computedtomography (CT) and thresholding for MR, for example. The body part canbe a breast, a lung or a liver, for example. The medical image can be anMR image or a CT image, for example.

A Reeb graph of the region of interest is calculated (420). As describedabove, the Reeb graph is calculated by defining a function ƒ on theobject M (i.e., the region of interest). The function ƒ can be theisolation measure (μ) or a radial function, for example.

The isolation measure is computed for each voxel in the region ofinterest in accordance with Equation 1 above. It is noted that, inEquation 1 as used here, v is a point of S at which we want to calculatethe functional value of μ, p is any point of S, and g(v,p) is a functionthat returns a distance between v and p of S, S is a portion of theregion of interest and μ(v) is a mean of a distance from v to all pointsof S. S can be a surface of the region of interest.

The radial function is computed for each voxel in the region of interestin accordance with the following equation:μ(v)=d(v,c)   (2)where d(v,c) is a Euclidean distance between v and c, c is a point ofthe region of interest, such as its centroid or the center of acircumscribed sphere, which represents the region of interest, and v isany point of the region of interest at which we want to calculate thefunctional value of μ.

A determination is made as to whether the region of interest is amalignant lesion candidate based on a shape characteristic of the Reebgraph (430). This is done in a variety of ways. For example, in onetechnique, the number of branches in the Reeb graph is used to determineif the region of interest is a malignant lesion candidate. Thus, if thenumber of branches is above a threshold, such as 20 branches, forexample, the region of interest is marked as a malignant lesioncandidate. In another technique, a number of branches in the Reeb graphthat are above a certain length, such as the average of all the branchlengths, for example, is compared against a threshold, and if the numberis above the threshold, the region of interest is marked as a malignantlesion candidate.

In yet another technique, an average of all the isolation measures canbe obtained and divided by a square root of the volume of the region ofinterest. If this value is above a threshold, such as, 0.5, for example,the region of interest is marked as a malignant lesion candidate.Instead of dividing the average of the isolation measures by the squareroot of the volume of the region of interest, a median or a maximum ofthe isolation measures can be divided by the square root or the cubicroot of the volume of the region of interest. Similarly, the average ofthe isolation measures can be divided by the cubic root of the volume ofthe region of interest. Further, a combination, either linear (⅓, ⅓ and⅓) or non-linear (½, ¼ or ⅓), of the average, median and maximumisolation measures can be divided by the square or cubic root of thevolume of the region of interest and used to determine whether theregion of interest is a malignant lesion candidate.

It is to be understood that the above-described isolation measuretechnique can be used to supplement the malignancy determination made bythe branches or it can be used without constructing a Reeb graph todetermine whether a region of interest should be marked as a malignantlesion candidate. In this case, the method as shown in FIG. 5 may beemployed. As shown in FIG. 5, similar to that shown in FIG. 4, a regionof interest is found in a medical image of a body part (510). However,instead of calculating a Reeb graph for the region of interest, anisolation measure is calculated for each voxel in the region of interest(520). A determination is made as to whether the region of interest is amalignant lesion candidate by using the isolation measures, by using thetechniques just described (530).

The thresholds described above can be determined by training aclassifier on relevant sets of image data.

The methods described with reference to FIGS. 4 and 5 are automaticallyperformed by a computer, for example.

A system in which exemplary embodiments of the present invention may beimplemented will now be described with reference to FIG. 6.

As shown in FIG. 6, the system includes a scanner 605, a server 615 anda radiologist workstation 610 connected over a wired or wireless network(indicated by the arrows). The scanner 605 may be an MR or CT scanner,for example.

The server 615 includes, inter alia, a central processing unit (CPU)620, a memory 625 and a shape analysis module 630 that includes programcode for executing methods in accordance with exemplary embodiments ofthe present invention.

The radiologist workstation 610 includes a computer, which may alsoinclude a shape analysis module that includes program code for executingmethods in accordance with exemplary embodiments of the presentinvention, and appropriate peripherals, such as a keyboard and display,and is used to operate the system. For example, the radiologistworkstation 610 may communicate directly with the scanner 605 so thatimage data collected by the scanner 605 can undergo real-time shapeanalysis and be viewed on its display. The radiologist workstation 610may also communicate directly with the server 615 to access previouslyprocessed image data, such as that which has undergone our shapeanalysis, so that a radiologist can manually verify the results of theshape analysis.

It is to be understood that the present invention may be implemented invarious forms of hardware, software, firmware, special purposeprocessors, or a combination thereof. In one embodiment, the presentinvention may be implemented in software as an application programtangibly embodied on a program storage device (e.g., magnetic floppydisk, RAM, CD ROM, DVD, ROM, and flash memory). The application programmay be uploaded to, and executed by, a machine comprising any suitablearchitecture.

It should also be understood that because some of the constituent systemcomponents and method steps depicted in the accompanying figures may beimplemented in software, the actual connections between the systemcomponents (or the process steps) may differ depending on the manner inwhich the present invention is programmed. Given the teachings of thepresent invention provided herein, one of ordinary skill in the art willbe able to contemplate these and similar implementations orconfigurations of the present invention.

It is to be further understood that the above description is onlyrepresentative of illustrative embodiments. For convenience of thereader, the above description has focused on a representative sample ofpossible embodiments, a sample that is illustrative of the principles ofthe invention. The description has not attempted to exhaustivelyenumerate all possible variations. That alternative embodiments may nothave been presented for a specific portion of the invention, or thatfurther undescribed alternatives may be available for a portion, is notto be considered a disclaimer of those alternate embodiments. Otherapplications and embodiments can be implemented without departing fromthe spirit and scope of the present invention.

It is therefore intended, that the invention not be limited to thespecifically described embodiments, because numerous permutations andcombinations of the above and implementations involving non-inventivesubstitutions for the above can be created, but the invention is to bedefined in accordance with the claims that follow. It can be appreciatedthat many of those undescribed embodiments are within the literal scopeof the following claims, and that others are equivalent.

What is claimed is:
 1. A method for analyzing a shape of a region ofinterest in a medical image of a body part, comprising: collecting, by ascanner, the medical image of the body part; finding, by a processor, aregion of interest in the medical image; calculating, by the processor,a Reeb graph of the region of interest; and determining, by theprocessor, whether the region of interest is a malignant lesioncandidate based on a shape characteristic of the Reeb graph.
 2. Themethod of claim 1, wherein the shape characteristic comprises a numberof branches in the Reeb graph, and when the number of branches is abovea threshold the region of interest is a malignant lesion candidate. 3.The method of claim 1, wherein the shape characteristic comprises anumber of branches in the Reeb graph that are above a length, and whenthe number of branches is above a threshold the region of interest is amalignant lesion candidate.
 4. The method of claim 1, furthercomprising: choosing a function from which to calculate the Reeb graph.5. The method of claim 4, wherein the function is an isolation measurethat is computed for each voxel in the region of interest.
 6. The methodof claim 5, wherein the shape characteristic comprises a value that isobtained by dividing a value obtained from the isolation measures by apower of a volume of the region of interest, and when the value of theshape characteristic is above a threshold the region of interest is amalignant lesion candidate.
 7. The method of claim 6, wherein the valueobtained from the isolation measures is an average of the isolationmeasures, a median of the isolation measures, a maximum of the isolationmeasures or a combination of the average, median or maximum of theisolation measures.
 8. The method of claim 6, wherein the power of thevolume of the region of interest is a square root or a cubic root of thevolume of the region of interest.
 9. The method of claim 5, wherein theisolation measure is represented by:μ(v)=∫_(pεS) g(v,p)dS, where v is a point of S at which to calculate μ,p is a point of S, g(v,p) is a function that returns a distance betweenv and p of S, S is a portion of the region of interest and μ(v) is amean of a distance from v to all points of S.
 10. The method of claim 9,wherein S is a surface of the region of interest.
 11. The method ofclaim 9, wherein the distance is a geodesic distance or a Euclideandistance.
 12. The method of claim 4, wherein the function is a radialfunction that is computed for each voxel in the region of interest. 13.The method of claim 12, wherein the radial function is represented by:μ(v)=d(v,c), where d(v,c) is a Euclidean distance between v and c, c isa point of the region of interest and v is a point of the region ofinterest at which to calculate μ.
 14. The method of claim 13, wherein cis a centroid or a center of the region of interest.
 15. The method ofclaim 1, wherein the medical image comprises a magnetic resonance imageor a computed tomography image.
 16. The method of claim 1, wherein thebody part comprises a breast, a lung or liver.
 17. A system foranalyzing a shape of a region of interest in a medical image of a bodypart, comprising: a memory device for storing a program; a processor incommunication with the memory device, the processor operative with theprogram to: find a region of interest in the medical image; calculate aReeb graph of the region of interest; and determine whether the regionof interest is a malignant lesion candidate based on a shapecharacteristic of the Reeb graph.
 18. A method for analyzing a shape ofa region of interest in a medical image of a body part, comprising:collecting, by a scanner, the medical image of the body part; finding,by a processor, a region of interest in the medical image; calculating,by processor, an isolation measure for each voxel in the region ofinterest; and determining, by the processor, whether the region ofinterest is a malignant lesion candidate by using the isolationmeasures.
 19. A system for analyzing a shape of a region of interest ina medical image of a body part, comprising: a memory device for storinga program; a processor in communication with the memory device, theprocessor operative with the program to: find a region of interest inthe medical image; calculate an isolation measure for each voxel in theregion of interest; and determine whether the region of interest is amalignant lesion candidate by using the isolation measures.